We propose to design, test, and implement new methods for estimating carrier probabilities, penetrance, and allele frequency for cancer predisposition syndromes. We will use Markov Chain Monte Carlo (MCMC) methods and related sample-path methods. Pedigree and disease data will be obtained from the Utah Population Database (UPDB), which consists of more than one million population-based genealogical records linked to cancer and follow-up data. We will begin by simulating the occurrence of disease among members of the pedigrees and attempting to estimate the relevant genetic parameters with MCMC methods. Once we have successfully estimate carrier probabilities, we will extend the methods to estimate penetrance and allele frequency. When the MCMC algorithm is able to correctly estimate all the desired parameters, we will use it to generate estimates of carrier probabilities, penetrance, and allele frequency using actual UPDB data on breast, prostate, colorectal, and ovarian cancer.